x*(60-x)=600

Solution for x*(60-x)=600 equation:

x(60-x)=600

We move all terms to the left:

x(60-x)-(600)=0

We add all the numbers together, and all the variables

x(-1x+60)-600=0

We multiply parentheses

-1x^2+60x-600=0

a = -1; b = 60; c = -600;
Δ = b2-4ac
Δ = 602-4·(-1)·(-600)
Δ = 1200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{3}}{2*-1}=\frac{-60-20\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{3}}{2*-1}=\frac{-60+20\sqrt{3}}{-2}
$